Nuclear chemistry: radioactive decay kinetics and half-life

28 questions on Nuclear chemistry: radioactive decay kinetics and half-life from the Atomic Structure chapter: 5 NEET level, 12 JEE Main, 11 JEE Advanced. Each one opens with its answer and solution.

• A radioactive nuclide has a half-life of 20 min. What fraction of a sample remains undecayed after 60 min? NEET level
• Uranium-238 (Z=92) decays by emission of one alpha particle. The daughter nuclide is NEET level
• Which statement about the radioactive decay of a nuclide is correct? NEET level
• The nuclide ^32_15P decays by beta^- emission. The daughter nuclide is NEET level
• One curie is defined as 3.7x10^10 disintegrations per second. The activity of a 2.0 mCi source, in disintegrations per second, is NEET level
• A sample initially of 16 g of a radioisotope is found to have only 2.0 g of it left after 24 days. The half-life of the isotope, in days, is JEE Main level
• The half-life of a radon isotope is 3.8 days. Using ln 2=0.693 and 1 day=86400 s, its decay constant in s^-1 is closest to JEE Main level
• The nuclide ^238_92U finally changes to the stable ^206_82Pb through a series of alpha and beta^- emissions. The numbers of alpha and beta^- particles emitted a... JEE Main level
• The fraction of a radioactive sample that has decayed after 2.5 half-lives is closest to JEE Main level
• Samples A and B contain equal numbers of atoms initially. The half-lives are 10 min for A and 20 min for B. The ratio (activity of A) : (activity of B) after 40... JEE Main level
• A nuclide has a half-life of 10.0 hours. Its mean (average) life, in hours, is closest to JEE Main level
• Tritium has a half-life of 12.3 years. A sealed sample initially holds 8.0 mg of tritium. Taking decay as the only loss, find the mass of tritium left after 40 ... JEE Main level
• The half-life of ^226Ra is 1600 years. Take molar mass 226 g mol^-1, N_A=6.022x10^23, ln2=0.693 and 1 year=3.156x10^7 s. The activity of 1.00 g of radium-226, e... JEE Main level
• The counting rate of a radioisotope falls from 800 to 100 counts per minute. Its decay constant is 0.0385 h^-1. Use ln 2=0.693. The time taken, in hours, to the... JEE Main level
• A wooden relic shows a carbon-14 activity equal to 60% of that of living wood. Taking the half-life of ^14C as 5730 years and using exact logarithms, its age in... JEE Main level
• Which of the following statements about nuclear transformations are correct? JEE Main level
• A radioisotope with half-life 10 min undergoes first-order decay. Take ln2=0.693. Which statements are correct? JEE Main level
• A nuclide decays by two independent parallel modes: alpha emission with partial half-life 20 h and beta^- emission with partial half-life 30 h. Starting from N_... JEE Advanced level
• A rock sample contains ^238U and its final decay product ^206Pb in the mole ratio Pb:U=0.25:1. Assuming no lead was present initially and no loss of either, and... JEE Advanced level
• Nuclides A and B have half-lives of 2 h and 6 h respectively, and their activities are equal at t=0. At what time is the activity of B twice that of A? JEE Advanced level
• A sample of N_0 atoms has a half-life of 10 min. The number of atoms that decay between t=15 min and t=30 min is closest to JEE Advanced level
• A source holds 2.10 mg of ^210Po (molar mass 210 g mol^-1, half-life 138.4 days, N_A=6.022x10^23). The number of atoms that decay in the first 100 days, in unit... JEE Advanced level
• ^40K has a total half-life of 1.25x10^9 years, and only 10.7% of its decays produce ^40Ar (the rest give ^40Ca). A mineral had no argon at formation and now has... JEE Advanced level
• A mixture has two radioisotopes. Nuclide P has half-life 12 min and initial activity 2400 dps; nuclide Q has half-life 48 min and initial activity 100 dps. Afte... JEE Advanced level
• For a first-order radioactive decay with half-life t_1/2 and mean life tau, which statements are correct? JEE Advanced level
• The thorium series starts with ^232_90Th and ends with stable ^208_82Pb. Which statements are correct? JEE Advanced level
• Samples X and Y contain equal numbers of atoms at t=0. The half-life of X is 10 days and that of Y is 20 days. Which statements are correct? JEE Advanced level
• A sample has 1.6x10^20 atoms of a nuclide of half-life 8.0 days. Use ln2=0.693 and 1 day=86400 s. Which statements are correct? JEE Advanced level